Centrifuge Calculator

Centrifuge Calculator converts rotor speed in RPM to RCF in × g and back for any rotor radius, with k factor, equal run times, a rotor speed limit check and a tube balance diagram.

What the Centrifuge Calculator Solves

The Centrifuge Calculator has four modes under Solve For. It finds RCF in × g from RPM, the RPM for a required RCF, the rotor radius that links a speed to a force, and the speed that keeps the same RCF on a new rotor.

The default run is a 24-place microcentrifuge rotor with an 8.4 cm radius at 12,000 RPM, which gives 13,523 × g. The same rotor at its 15,000 RPM rating gives 21,130 × g. That is the maximum RCF listed for the Eppendorf 5424 with its standard 24-place rotor.

Four result cards sit under the main answer. The first gives the acceleration in m/s² with the tip speed. The second gives the force at the top of the tube and the k factor with a pelleting time. The third checks the run against the rotor speed limit, and the fourth shows a loading pattern that balances your tube count.

RPM to RCF Formula

Relative centrifugal force is the acceleration at the tube divided by standard gravity. With the speed in RPM and the radius in centimeters, it reduces to the formula printed by Sigma-Aldrich and by most rotor manuals.

$$RCF = 1.118 \times 10^{-5} \times r \times N^2$$

Here r is the radius in centimeters and N is the rotor speed in RPM. The constant comes from turning RPM into radians per second and dividing by standard gravity, which is 980.665 cm/s².

$$\frac{(\pi / 30)^2}{980.665} = 1.118 \times 10^{-5}$$

Some charts write the same formula as 11.18 × r × (RPM ÷ 1000)². With the radius in millimeters the constant is 1.118 × 10⁻⁶, and with inches it is 2.84 × 10⁻⁵. The Centrifuge Calculator accepts mm, cm, m, inches and feet, then converts the radius to centimeters before it applies the formula.

Speed is squared, so doubling the RPM gives four times the RCF. Radius is not squared, so doubling the radius only doubles the RCF. For 15,000 RPM at 8.4 cm the sum is 1.118 × 10⁻⁵ × 8.4 × 15,000², which comes to 21,130 × g.

RCF to RPM Formula

Most protocols state a force such as 16,000 × g, while many centrifuges only take a speed. Set Solve For to RPM from RCF, then enter the × g and the radius of your own rotor. The Centrifuge Calculator rearranges the same formula for speed.

$$N = \sqrt{\frac{RCF}{1.118 \times 10^{-5} \times r}}$$

For 16,000 × g on the 8.4 cm rotor the answer is 13,053 RPM. A frequent search is 1000 xg to RPM, and that works out to 3,263 RPM at 8.4 cm or 2,991 RPM at 10 cm. Used as a g to RPM calculator for an Eppendorf 5424, the entry is 8.4 cm and the × g from your method.

The force box also takes m/s² and ft/s². A centrifugal acceleration from a physics problem can go in without converting it to × g first, and the speed box accepts rev/s and rad/s as well as RPM.

Centrifuge Calculator RPM and RCF Chart

No RPM has a single × g value, because the answer changes with the rotor radius. The first table gives the RCF for the speeds people look up most, at four radii. The 8.4 cm column matches the default rotor in the tool above.

The second table runs the other way and gives the speed to set for a required force. Round the result to the nearest step your centrifuge display allows, and check it against the rotor’s rated speed before the run.

The answers below cover the single conversions searched most often. Each one uses the two formulas above, so the Centrifuge Calculator returns the same figure when you enter the radius shown.

How do I convert 15000 RPM to g?

Multiply 1.118 × 10⁻⁵ by the rotor radius in centimeters, then by 15,000 squared. At 8.4 cm that is 21,130 × g. At 10 cm it is 25,155 × g, and a small 5 cm rotor gives only 12,578 × g at the same speed.

What is 3000 RPM in g, and 12000 RPM in RCF?

At a 10 cm radius, 3,000 RPM is 1,006 × g, which makes a handy rule of thumb. At 8.4 cm it drops to 845 × g. For 12,000 RPM the RCF is 13,523 × g at 8.4 cm, 16,099 × g at 10 cm and 24,149 × g at 15 cm.

How much is 400 RCF in RPM?

400 × g needs 2,064 RPM at 8.4 cm, 1,892 RPM at 10 cm and 1,544 RPM at 15 cm. The gentler 200 × g used for many cell spins is 1,459 RPM at 8.4 cm. Going up, 4,000 × g is 6,526 RPM and 10,000 × g is 10,319 RPM on the same rotor.

Is 1000 g the same as 1000 RCF?

They are the same thing. RCF is written as a multiple of standard gravity, so 1,000 RCF, 1,000 × g and 1,000 g all mean an acceleration of 9,807 m/s². The g here is gravity and not grams, which is why methods print it as × g.

What is 1 RPM equal to?

One RPM is one turn per minute. That equals 0.01667 revolutions per second, or 0.1047 radians per second. As a force it is almost nothing, since 1 RPM at a 10 cm radius gives 0.0001118 × g. RCF only becomes useful at hundreds of RPM.

Which is higher, RPM or RCF?

It depends on speed and radius. The two numbers are equal when the RPM is 89,445 divided by the radius in centimeters. On an 8.4 cm rotor that crossover is 10,648 RPM. Below it the RPM figure is larger, and above it the RCF figure is larger.

Which Rotor Radius to Enter

The radius is the distance from the rotor axis to a point in the tube. Hettich defines the rotor radius as the distance from the axis to the bottom of the tube. Rotor data sheets use that maximum radius for the maximum RCF, so it is the figure to enter in Rotor Radius.

The force is not the same along the tube, and it falls in a straight line toward the axis. Open Tube, Time and Limit and enter the minimum radius, which is the distance to the top of the liquid. With 5.8 cm, the tube top sees 9,338 × g while the tip sees 13,523 × g, and the average is 11,430 × g.

Rotor shape changes these radii. Beckman Coulter notes that fixed-angle rotors commonly hold tubes at 25° to 40° and reach higher speeds. Swinging-bucket rotors let the tube swing out flat, which gives a longer path from the top of the liquid to the pellet.

Take both radii from the rotor manual, because adapters and shorter tubes move the sample closer to the axis. A method that names average RCF needs the average radius entered instead of the maximum, or the speed will come out too low.

The Rotor Radius mode works backward from a speed and a force. It answers which radius gives 16,000 × g at 12,000 RPM, and the result is 9.94 cm, or 99.4 mm and 3.91 in. That helps when choosing a rotor for a method or checking one with a worn label.

Same RCF on a New Rotor

Matching the RPM between two centrifuges does not match the force. Set Solve For to Same RCF on a New Rotor, then enter the original radius and speed with the radius of the new rotor. The Centrifuge Calculator holds the × g fixed and returns the new speed.

$$N_2 = N_1 \times \sqrt{\frac{r_1}{r_2}}$$

A run at 12,000 RPM on an 8.4 cm rotor gives 13,523 × g. A larger 9.5 cm rotor needs only 11,284 RPM for the same force. Going the other way, halving the radius raises the speed by a factor of 1.414, so a 4.2 cm rotor would need 16,971 RPM.

Matching the force does not fully match the run, because two rotors rarely share the same path length. Enter the Original Min Radius and the tool also returns a matched run time. It scales the original time by the ratio of the two k factors, which the next section explains.

$$t_2 = t_1 \times \frac{k_2}{k_1}$$

With the default entries, the original rotor has a k factor of 651.5 and the new 9.5 cm rotor at 11,284 RPM has 981.6. The larger rotor has a longer liquid path at a lower speed, so a 10 minute run becomes 15 min 4 s. The speed limit card, the chart and the step-by-step working all use that matched time.

That is the reason to record × g with the rotor model in a method, and not RPM alone. Anyone repeating the work on a different centrifuge can then set the speed that gives the same force on their own rotor.

Run Time and the k Factor

The k factor, also called the clearing factor, rates how fast a rotor pellets a sample. It combines the speed with the path a particle travels from the minimum radius to the maximum radius. A lower k factor means a shorter run.

$$k = \frac{2.533 \times 10^{11} \times \ln(r_{max} / r_{min})}{N^2}$$

The two radii share any unit and N is in RPM. The run time in hours is the k factor divided by the particle’s sedimentation coefficient in Svedberg units, as set out in Beckman Coulter’s k factor note.

$$t = \frac{k}{S}$$

Beckman’s example is bovine serum albumin at 4.4 S in a Type 70.1 Ti rotor with a k factor of 36, which takes 8 hours 11 minutes. Enter your own particle in the Sedimentation Coeff. field under Tube, Time and Limit, and the second card shows the k factor with the pelleting time beside it.

The default run in the Centrifuge Calculator has a k factor of 651.5 at 12,000 RPM, and the field starts at 70 S for a bacterial ribosome. The card reads 651.5 · 9 h 18 min, because 651.5 ÷ 70 comes to 9.3 hours.

That gap explains the division of work between machines. A microcentrifuge pellets cells and precipitates in minutes, because they are thousands of times heavier than a ribosome. Ribosomes and smaller particles go to an ultracentrifuge with a far lower k factor.

For one rotor, the k factor changes with the inverse square of speed, so run time × RPM² stays constant for equal pelleting. A 10 minute run at 12,000 RPM equals 6 min 24 s at 15,000 RPM or 40 minutes at 6,000 RPM. The RPM to RCF Chart inside the Centrifuge Calculator lists this equal run time on every speed row.

The Rotor Speed Limit field guards the top end. The default run sits at 80% of a 15,000 RPM limit. An answer above the limit turns the card red, and the tool gives the longer run at the limit that does the same work. A rotor must never be run above its rated speed.

Centrifugal Acceleration and Tip Speed

The first result card of the Centrifuge Calculator restates the answer for physics work. The centrifugal acceleration formula is the angular velocity squared times the radius, with the angular velocity in radians per second and the radius in meters.

$$a = \omega^2 \times r$$

At 12,000 RPM the angular velocity is 1,257 rad/s, and 13,523 × g is 132,620 m/s². RPM converts to rad/s by multiplying by 0.1047. The Angular Velocity Calculator and the Angular Frequency Calculator handle the other speed units.

RCF is an acceleration ratio and not a force in newtons. The outward force is the mass times the acceleration. A 2 g tube at 13,523 × g pushes outward with 265 N, about the weight of 27 kg. The Centrifugal Force Calculator works that out for any mass.

Tip speed answers what speed an RPM really is. It is the distance around the circle at the tube bottom times the turns per second. The table uses the 8.4 cm rotor, and a larger rotor is faster at the tip for the same RPM.

To go from RPM to km/h directly, multiply 0.00377 by the radius in centimeters and by the RPM. For miles per hour the factor is 0.00234. Both come from the circumference of the circle and the number of minutes in an hour.

$$v = 0.00377 \times r \times N$$

The card shows m/s and km/h when the radius is in metric units. Enter the radius in inches or feet and it switches to ft/s and mph. The same rotor entered as 3.307 in at 12,000 RPM reads 346.3 ft/s (236.1 mph).

A 10 minute run at 12,000 RPM turns the rotor 120,000 times, which is about 754,000 radians on the Angular Displacement Calculator. A rotor that reaches 15,000 RPM in 15 seconds has an angular acceleration of 105 rad/s², a sum the Angular Acceleration Calculator does from the two speeds and the time.

The spin a rotor stores is its angular momentum, which is why a heavy rotor takes longer to brake than a light one. The Angular Momentum Calculator finds it from the moment of inertia, and the Rotational Motion Calculators hub lists the related tools.

How to Balance 3 or 4 Tubes

An unbalanced rotor vibrates and can damage the drive. The Tube Balance section of the Centrifuge Calculator takes the number of rotor positions and the tubes you need to spin. It reports whether that count balances alone and draws the positions to load.

The rule comes from a proof by Gary Sivek. Equal tubes balance in a rotor only when the tube count and the number of empty positions can both be written as sums of the prime factors of the position count. For 24 positions those factors are 2 and 3.

So 3 tubes balance in a 24-place rotor as a triangle at positions 1, 9 and 17. Four tubes balance at positions 1, 7, 13 and 19, or as any two opposite pairs. Five tubes balance as a triangle plus an opposite pair. Only 1 tube and 23 tubes never balance, and each needs one blank.

An 8-place rotor is the awkward one, since its only prime factor is 2 and every odd count needs a blank. A 6-place rotor takes 3 tubes as a triangle in every second position, and 4 tubes as two opposite pairs.

A blank is a tube of the same type filled with water to the same weight as the samples. Beckman Coulter’s balancing guide requires opposing loads to match within the tolerance in the centrifuge manual. It also says a swinging-bucket rotor must never run with buckets missing.

The pattern assumes one ring of evenly spaced positions and tubes of equal mass. A rotor with an inner and an outer row needs each row balanced on its own, and tubes of different fill levels must be paired by weight first.

Centrifuge Speeds, Types and Uses

The basic principle of centrifugation is faster settling. A spinning rotor replaces gravity with a field thousands of times stronger. Denser particles move outward through the liquid and collect at the tube bottom as a pellet, and the settling rate rises in step with the RCF.

How many RPM does a centrifuge run at?

It depends on the class of machine. Beckman Coulter groups its range into three types, which are benchtop centrifuges, high-speed centrifuges and ultracentrifuges. Large-volume machines run slowest, and the Avanti J-HC spins 9 liters at 5,000 RPM and 7,480 × g.

A microcentrifuge such as the Eppendorf 5424 reaches 15,000 RPM and 21,130 × g. The high-speed Avanti JXN-30 reaches 30,000 RPM and more than 100,000 × g. The maximum speed of a centrifuge belongs to ultracentrifuges, and the Optima MAX-XP runs at up to 150,000 RPM and more than 1,000,000 × g.

Why centrifuge at 4 degrees?

A rotor spinning in air heats up from friction, and the sample warms with it. Proteins, enzymes and RNA break down faster when warm, so many methods call for 4 °C. Refrigerated models are built for this, and the Eppendorf 5424 R covers −10 °C to +40 °C and holds 4 °C at its maximum speed.

How do you calculate centrifuge capacity and size?

Capacity is the number of rotor positions times the tube volume. A 24-place rotor with 2 mL tubes holds 48 mL in one run. To size a centrifuge, start with the highest × g your methods need, then the tube size and how many tubes go in each run.

In the Centrifuge Calculator, enter the required × g and the radius of the rotor you are considering. If the RPM that comes back is above the rotor’s rating, that rotor cannot do the job. Cooling is the last check, for samples that must stay at 4 °C.

What are five uses of a centrifuge?

Labs use one to pellet cells and bacteria from culture, and to split blood into plasma and cells. It also collects DNA, RNA and protein precipitates, clears debris from a lysate, and separates organelles or viruses on a density gradient in an ultracentrifuge.